\(U(1)_{\mu -\tau }\)  gauge symmetry is anomaly free even without
additional chiral fermions beyond the SM fermions [1]}, [2]}.
It has been frequently applied to models that explains some of these flavor anomalies.
Due to feature of flavor dependent symmetry, we often obtain flavor specific signals that can be
more testable through various experiments than the SM.
Moreover, since a new gauge boson does not directly interact with electrons up to small
knetic mixing, we can evade stringent constraints on the gauge coupling and
gauge boson mass from LEP (or ILC) easier than the other gauged models. Notice here that we have to consider a constraint of neutrino trident production in gauged \(U(1)_{\mu -\tau }\)  models [3]}, and we will discuss it in the main text. Also the muon \(g-2\)  within the \(U(1)_{\mu -\tau }\)  gauge
models was studied right after the BNL announcement  [4]}. And the PAMELA
\(e^+\)  excess was studied in the \(U(1)_{\mu -\tau }\) -charged dark matter with mass
\(\sim O(1)\)  TeV in Ref. [5]}.
